A New Technique for Estimating the Lower Bound of the Trust-Region Subproblem

Trust-region methods are popular for nonlinear optimization problems. How to determine the predicted reduction of the trust-region subproblem is a key issue for trust-region methods. Powell gave an estimation of the lower bound of the trust-region subproblem by considering the negative gradient direction. In this article, we give an alternate way to estimate the same lower bound of the trust-region subproblem.

A FILTER-TRUST-REGION METHOD FOR LC^1 UNCONSTRAINED OPTIMIZATION AND ITS GLOBAL CONVERGENCE

In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.

Projected gradient trust-region method for solving nonlinear systems with convex constraints

In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.

A nonmonotone adaptive trust-region algorithm for symmetric nonlinear equations

In this paper, we propose a nonmonotone adap-tive trust-region method for solving symmetric nonlinear equations problems. The convergent result of the presented method will be estab-lished under favorable conditions. Numerical results are reported.

A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION

The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.

A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques

The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some conditions.The authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration step.They analyze the optimization dynamics and convergence of the algorithm SUSD-TR.Details of the trial step and structure step are given.Numerical results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD direction.Their algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.

A TRUST-REGION METHOD FOR NONSMOOTH NONCONVEX OPTIMIZATION

We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a(probably nonconvex)smooth function and a(probably nonsmooth)convex function.The model function of our trust-region subproblem is always quadratic and the linear term of the model is generated using abstract descent directions.Therefore,the trust-region subproblems can be easily constructed as well as efficiently solved by cheap and standard methods.When the accuracy of the model function at the solution of the subproblem is not sufficient,we add a safeguard on the stepsizes for improving the accuracy.For a class of functions that can be“truncated”,an additional truncation step is defined and a stepsize modification strategy is designed.The overall scheme converges globally and we establish fast local convergence under suitable assumptions.In particular,using a connection with a smooth Riemannian trust-region method,we prove local quadratic convergence for partly smooth functions under a strict complementary condition.Preliminary numerical results on a family of Ei-optimization problems are reported and demonstrate the eficiency of our approach.

基于匹配信任度机制的移动传感网簇头更新算法

为解决移动传感网部署过程中存在的簇头节点更新质量不佳和节点生存率较低等不足,提出了一种基于匹配信任度机制的移动传感网簇头更新算法。首先,引入K-means算法,利用误差平方根函数来完成网络初始聚类,以快速定位聚类中心,提升聚类形成速度。随后,综合考虑备选簇头剩余能量、备选簇头与当前簇头的欧氏距离、备选簇头覆盖范围内节点总数3个因素,设计了基于匹配信任度的簇头更新方法,按权值对各因素进行平均分配,进而将信任度权值最高的节点作为备选簇头,从而选举出生存质量较高的节点。仿真实验表明,算法具有更高的网络稳定运行时间和簇头节点生存率,以及更低的节点故障概率。其中,网络稳定运行时间提升了80%以上,簇头节点生存率保持在90%以上,节点故障概率也较低,具有明显的优势。

STOCHASTIC TRUST-REGION METHODS WITH TRUST-REGION RADIUS DEPENDING ON PROBABILISTIC MODELS

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models.Especially,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the gradient used to define the latest model.The complexity results of the STRME method in nonconvex,convex and strongly convex settings are presented,which match those of the existing algorithms based on probabilistic properties.In addition,several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.

A Trust-region Algorithm for Nonlinear Constrained Optimization Problem

This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.

区域品牌信任对跨省旅游购物行为的影响研究--区域品牌类型的调节效应

区域品牌是跨省游客获取旅游商品信息的重要渠道,基于TPB理论探讨了区域品牌信任对跨省游客旅游商品购买意愿的影响机制。研究发现:区域品牌信任正向影响跨省游客购买态度和意愿,区域品牌信任和态度中介主观规范对购买意愿的影响;区域品牌类型调节了“主观规范→区域品牌信任”和“区域品牌信任→购买意愿”两条路径,当以区域旅游商品品牌为依托型时,区域品牌信任对购买意愿有显著影响,主观规范对区域品牌信任影响则更大。

Error bounds of Lanczos approach for trust-region subproblem

Because of its vital role of the trust-region subproblem （TRS） in various applications, for example, in optimization and in ill-posed problems, there are several factorization-free algorithms for solving the large-scale sparse TRS. The truncated Lanczos approach proposed by N. I. M. Gould, S. Lucidi, M. Roma, and P. L. Toint [SIAM J. Optim., 1999, 9： 504-525] is a natural extension of the classical Lanczos method for the symmetric linear system and eigenvalue problem and, indeed follows the classical Rayleigh-Ritz procedure for eigenvalue computations. It consists of 1） projecting the original TRS to the Krylov subspa^es to yield smaller size TRS＇s and then 2） solving the resulted TRS＇s to get the approximates of the original TRS. This paper presents a posterior error bounds for both the global optimal value and the optimal solution between the original TRS and their projected counterparts. Our error bounds mainly rely on the factors from the Lanczos process as well as the data of the original TRS and, could be helpful in designing certain stopping criteria for the truncated Lanczos approach.

地区社会信任对企业ESG表现的影响研究

高质量发展仍是我国经济发展的核心内容,提升企业的ESG表现有助于推动该目标实现。文章以2011—2021年沪深A股上市公司为样本,研究地区社会信任对企业ESG表现的影响。研究表明,地区社会信任能够显著提升企业的ESG表现。异质性分析发现,当公司为民营企业,公司所在地的法律制度不完善或者分析师关注度低时,社会信任对ESG表现的促进作用更加明显。进一步分析发现,地区社会信任主要通过缓解企业融资约束和降低代理成本途径,来促进企业进行ESG实践。以上发现有助于理解地区社会信任影响微观企业的作用机理,也为企业ESG表现的提升和我国ESG的发展路径提供了理论支持和经验证据。

MMC-HVDC交直流混联系统小扰动稳定域迭代求解和形态分析

随着高压直流输电技术的发展,区域电力系统将拓展为大规模交直流混联系统。因此,需要建立可以同时精确刻画交直流动态的大规模交直流混联系统模型来研究混联系统的动态与稳定性。文中考虑了交流侧和直流侧的详细动态,建立了异步联网的模块化多电平换流器型高压直流(MMC-HVDC)交直流混联系统的状态空间模型,给出了具体的解析解形式,并推导了多重迭代信赖域算法。所提算法建立了决策变量空间内的点与平衡点的映射关系,结合Hopf分岔识别边界,提出了一种多重迭代求解小扰动稳定域边界的方法。在利用Simulink仿真验证模型准确性后,以发电机出力作为决策变量绘制了交直流混联系统稳定域,利用特征根和参与因子定量研究了直流失稳和交流失稳的机理以及控制策略和控制参数对稳定域边界的影响。对比分析了多区域的混联系统与交流系统的稳定域,结果表明换流站和直流网络的引入可能使多区域系统稳定域边界呈现多约束共同决定的近似分段线性拓扑特性。

非合作线谱声源分布式定位方法

非合作目标定位是水声定位领域的研究热点。为充分挖掘并利用各类可观测参数,提高非合作目标定位能力,提出一种基于目标频率变化信息的非合作目标定位方法。该方法针对匀速直线运动目标的定位问题,首先根据多普勒频移原理,建立观测频率与目标辐射频率、目标运动速度、位置之间的函数映射关系,利用最小均方准则建立目标函数,通过优化算法估计分布式定位系统中各个测量单元与目标运动轨迹的致近点距离,最后综合各观测节点的测距结果,构建几何定位模型,求得目标运动轨迹的解析解。通过仿真分析,证明了该方法的有效性,并指出了该方法需要目标通过与各测量单元的致近点才能获得较好的距离估计能力。文中分析了不同频率估计精度对定位精度的影响,结果表明,提出的定位方法对测频精度具有一定的容限,是一种高精度的非合作线谱声源定位方法。

A NEW TRUST-REGION ALGORITHM FOR FINITE MINIMAX PROBLEM

In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different with the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the effiency of the new method.

基于信赖域策略寻优的后退虚源法面源氡扩散模型

在使用面源高斯扩散模型模拟铀尾矿库核素氡扩散浓度时,面源积分模型计算复杂,后退虚源模型模拟结果不准确且不具备保守性。针对上述问题,提出了基于信赖域算法的函数与参数寻优方法。通过构建近似后退虚源模型的非线性函数集,将面源积分模型与函数库中每个函数模拟值之间的误差作为目标函数,在信赖域策略下调用函数库并迭代寻优,输出函数库中最优函数与其最优参数值。通过浓度分布对比与拟合测验得出:优化函数在近源处的模拟值略大于面源积分模型,表明优化函数具备一定的保守性;模拟值与面源积分模型的拟合决定系数在近源处高于0.91,大部分区域高于0.98,说明其模拟结果可靠;同时,优化函数保留了后退虚源模型计算简便的特点。此外,根据误差的影响因素分析,优化函数对于面源面积和大气稳定度不变时,能适应其他参数的变化,大大简化了实际氡浓度评估时的计算过程。

A necessary and sufficient condition of convexity for SOC reformulation of trust-region subproblem with two intersecting cuts

We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation with second-order-cone reformulation(SDPR-SOCR) is a tight relaxation. In the more complicated "intersecting" case, which is discussed in this paper, so far there is no result except for a counterexample for the SDPR-SOCR. We present a necessary and sufficient condition for the SDPR-SOCR to be a tight relaxation in both the "nonintersecting" and "intersecting" cases. As an application of this condition, it is verified easily that the "nonintersecting" SDPR-SOCR is a tight relaxation indeed. Furthermore, as another application of the condition, we prove that there exist at least three regions among the four regions in the trust-region ball divided by the two intersecting linear cuts, on which the SDPR-SOCR must be a tight relaxation. Finally, the results of numerical experiments show that the SDPR-SOCR can work efficiently in decreasing or even eliminating the duality gap of the nonconvex extended trust-region subproblem with two intersecting linear inequalities indeed.

A Subspace Version of the Powell–Yuan Trust-Region Algorithm for Equality Constrained Optimization

This paper studied subspace properties of the Celis–Dennis–Tapia(CDT)subproblem that arises in some trust-region algorithms for equality constrained optimization.The analysis is an extension of that presented by Wang and Yuan(Numer.Math.104:241–269,2006)for the standard trust-region subproblem.Under suitable conditions,it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current iteration.Based on this observation,a subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results arealso reported.